Objectives To create a linked-chain data structure To understand how to apply mathematical algorithms...

 

 



 

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Objectives • To create a linked-chain data structure • To understand how to apply mathematical algorithms Instructions For this program, you will implement two classes, one representing a single term, and one representing a polynomial. The Polynomial class must support the following: . 2 constructors . . o A constructor that takes two parameters: exponent and coefficient A copy constructor A print method Recall that if we have, for example, the term 3x², then 3 is the coefficient, and 2 is the exponent Operations 0 o The method should print the polynomial This constructor will take, as its argument, a reference to the Polynomial which it is supposed to copy . clone method This method is inherited from Object You must override it to work correctly It copies and returns a new Polynomial object, which is a (deep) copy of the original that it is cloning . . o A Term node reference to point to the next node in the chain of linked nodes o Methods to get and set the exponent, coefficient, and next node The Polynomial class must keep track of the first node in the polynomial. Therefore one of its fields should be a Term reference Although the two-parameter constructor only allows a Polynomial to contain a single term to start off with, the add method allows for terms and larger polynomials to be combined, and the copy constructor and clone methods allow for creation and copying of larger polynomials When the add method is called, the polynomial that is passed in is added to whatever exists in the current polynomial For example: If polyA contains the polynomial 3x²+2x+5 and poly8 contains 3x+2, then the polyA will become: 3x² + 5x+7 Each of the terms, 3x², 5x, and 7 have their own Term object associated with them. They are in a linked chain. You can assume that all Polynomials will maintain and be passed in by standard form. For example, the polynomial inputs to add, or that will be copied, etc. - will always keep the form 3x² + 2x + 5, not something else like 2x+5+ 3x². The highest term always comes first, then second highest, etc. Some polynomials might have "missing" terms. Not all will be given with all the intermediate terms. For example, 5x² + 2x would be a perfectly acceptable polynomial, even though there is no x² term or constant o Note that a constant would be represented in a Term object by having an exponent of 0, because 2x⁰ = 2, since anything to the nower 0 is 1 we would have ?*1=2 Note that a constant would be represented in a Term object by having an exponent of 0, because 2x = 2, since anything to the power 0 is 1, we would have 2*1 = 2. • A visual of a polynomial chain would look like this: . To represent the polynomial 3x² + 2x + 3, we would have polyRef→[3x²] → [2x] → [3]→null For 4x³ - 2x you would have: polyRef →[4x³] → [-2x]→null Notice that the "minus" is represented by having the coefficient of the second term in the polynomial set to a -2. Major Hints / Design considerations: While coming up with a solution might seem daunting, especially when you must copy, add, or clone an entire arbitrary-length polynomial, keep some things in mind: o Like-terms are combined when add is called E.g., if you have the two polynomials polyA and polyB, and they each have respective x² terms, you add the coefficients If you are traversing a polynomial, you know you're finished when you reach null Objectives • To create a linked-chain data structure • To understand how to apply mathematical algorithms Instructions For this program, you will implement two classes, one representing a single term, and one representing a polynomial. The Polynomial class must support the following: . 2 constructors . . o A constructor that takes two parameters: exponent and coefficient A copy constructor A print method Recall that if we have, for example, the term 3x², then 3 is the coefficient, and 2 is the exponent Operations 0 o The method should print the polynomial This constructor will take, as its argument, a reference to the Polynomial which it is supposed to copy . clone method This method is inherited from Object You must override it to work correctly It copies and returns a new Polynomial object, which is a (deep) copy of the original that it is cloning . . o A Term node reference to point to the next node in the chain of linked nodes o Methods to get and set the exponent, coefficient, and next node The Polynomial class must keep track of the first node in the polynomial. Therefore one of its fields should be a Term reference Although the two-parameter constructor only allows a Polynomial to contain a single term to start off with, the add method allows for terms and larger polynomials to be combined, and the copy constructor and clone methods allow for creation and copying of larger polynomials When the add method is called, the polynomial that is passed in is added to whatever exists in the current polynomial For example: If polyA contains the polynomial 3x²+2x+5 and poly8 contains 3x+2, then the polyA will become: 3x² + 5x+7 Each of the terms, 3x², 5x, and 7 have their own Term object associated with them. They are in a linked chain. You can assume that all Polynomials will maintain and be passed in by standard form. For example, the polynomial inputs to add, or that will be copied, etc. - will always keep the form 3x² + 2x + 5, not something else like 2x+5+ 3x². The highest term always comes first, then second highest, etc. Some polynomials might have "missing" terms. Not all will be given with all the intermediate terms. For example, 5x² + 2x would be a perfectly acceptable polynomial, even though there is no x² term or constant o Note that a constant would be represented in a Term object by having an exponent of 0, because 2x⁰ = 2, since anything to the nower 0 is 1 we would have ?*1=2 Note that a constant would be represented in a Term object by having an exponent of 0, because 2x = 2, since anything to the power 0 is 1, we would have 2*1 = 2. • A visual of a polynomial chain would look like this: . To represent the polynomial 3x² + 2x + 3, we would have polyRef→[3x²] → [2x] → [3]→null For 4x³ - 2x you would have: polyRef →[4x³] → [-2x]→null Notice that the "minus" is represented by having the coefficient of the second term in the polynomial set to a -2. Major Hints / Design considerations: While coming up with a solution might seem daunting, especially when you must copy, add, or clone an entire arbitrary-length polynomial, keep some things in mind: o Like-terms are combined when add is called E.g., if you have the two polynomials polyA and polyB, and they each have respective x² terms, you add the coefficients If you are traversing a polynomial, you know you're finished when you reach null